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Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2004; 59:20192046 (DOI: 10.1002/nme.949)
A fast boundary cloud method for 3D exterior
electrostatic analysis
Vaishali Shrivastava and N. R. Aluru,
Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign,
Urbana, IL 61801, U.S.A.
SUMMARY
An accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic prob-
lems is presented here. BCM uses scattered points unlike the classical boundary element method
(BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines
the weighted least-squares approach for the construction of approximation functions with a boundary
integral formulation for the governing equations. A linear base interpolating polynomial that can vary
from cloud to cloud is employed. The boundary integrals are computed by using a cell structure
and different schemes have been used to evaluate the weakly singular and non-singular integrals.
A singular value decomposition (SVD) based acceleration technique is employed to solve the dense
linear system of equations arising in BCM. The performance of BCM is compared with BEM for
several 3D examples. Copyright 2004 John Wiley & Sons, Ltd.
KEY WORDS: meshless methods; boundary cloud method (BCM); fast algorithms; SVD; BEM;
exterior electrostatics
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